Overall Heat Transfer Coefficient (U)

Resistances in series add, and heat transfer borrows the electrical analogy wholesale: 1/U is the total resistance per unit area, the sum of the inside film, the metal, and the outside film. What falls out is the engineer's most useful insight: the largest resistance owns the answer. Take a steel exchanger tube, 3 mm of steel at k = 45 W/(m·K), water inside at hᵢ = 5000 and air outside at hₒ = 2000: 1/U = 0.000200 + 0.0000667 + 0.000500 = 0.000767, so U = 1304 W/(m²·K). Note that the steel, the only part you can see, contributes 9% of the resistance. Doubling the tube wall barely moves U; doubling the air-side film nearly doubles it.

That is why finned tubes exist. Air-side coefficients are typically 20–50 times worse than water-side ones, so every gas-to-liquid exchanger in the world grows fins on the gas side to buy back area rather than coefficient. The trap on real datasheets is area basis: U must be quoted against a stated area (usually the outside), and a U of 850 W/(m²·K) on inside area is not the same machine as 850 on outside area. When you see U and A on a drawing, check which surface A refers to before you believe the duty.